Question: Find the greatest common factor of $21$ and $28$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $21$ and $28$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}21 &=3\cdot7\\\\\\\\ 28&=2\cdot2\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}21 &=3\cdot7\\\\\\\\ 28&=2\cdot2\cdot7 \end{aligned}$ Each number shares the factor ${7}$, so the GCF is ${7}$. The greatest common factor of $21$ and $28$ is $7$.